{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:27:06Z","timestamp":1787329626718,"version":"build-2736575974"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that, using this condition, the iterative refinement algorithm terminates successfully. Additionally we provide an $O(n)$ algorithm that renumbers any simplex grid to fulfill this condition. Furthermore we conduct experiments to estimate the distance to the standard compatibility and also study the geometric quality of the produced meshes.<\/jats:p>","DOI":"10.1137\/17m1156137","type":"journal-article","created":{"date-parts":[[2018,11,20]],"date-time":"2018-11-20T12:35:20Z","timestamp":1542717320000},"page":"A3853-A3872","source":"Crossref","is-referenced-by-count":5,"title":["A Weak Compatibility Condition for Newest Vertex Bisection in Any Dimension"],"prefix":"10.1137","volume":"40","author":[{"given":"Martin","family":"Alk\u00e4mper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fernando","family":"Gaspoz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Kl\u00f6fkorn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,11,20]]},"reference":[{"key":"atypb1","first-page":"1","volume":"4","author":"Alk\u00e4mper M.","year":"2016","journal-title":"Arch. Numer. Software"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2016.12.003"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.15388\/Informatica.2015.36"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597323373"},{"key":"atypb5","first-page":"13","volume":"4","author":"Blatt M.","year":"2016","journal-title":"Arch. Numer. Software"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/07069047X"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/BF00181352"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20671-9_89"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1515\/cmam-2014-0013"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drv044"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2579"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-05591-6_61"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2010.05.046"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-97-00809-0"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2014.2342280"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-013-9192-4"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1134\/S0965542508090170"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(94)90034-5"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/0916014"},{"key":"atypb21","unstructured":"W. F. Mitchell,\n                      Unified Multilevel Adaptive Finite Element Methods for Elliptic Problems\n                      , Ph.D. thesis, Department of Computer Science, University of Illinois, Urbana, IL, 1988."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1063\/1.4951755"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2004.01.001"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19970930)40:18<3313::AID-NME214>3.0.CO;2-#"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00772-7"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1145\/2629697"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-01959-X"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684475"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1156137","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:24:24Z","timestamp":1787325864000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1156137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1156137"],"URL":"https:\/\/doi.org\/10.1137\/17m1156137","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}